Motion-Classification/BreathingAnalysis.html at master · swallace21/Motion-Classification · GitHub

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<!DOCTYPE html>
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<head><meta charset="utf-8" />
<title>BreathingAnalysis</title>

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<h1 id="A3---Bonus---cs2951-R">A3 - Bonus - cs2951-R<a class="anchor-link" href="#A3---Bonus---cs2951-R">&#182;</a></h1><p>Shaun Wallace
File: breathing.py
(Python 3.5.1 &amp; Anaconda 4, Mac OS X 10.9.5)</p>
<h5 id="Goal">Goal<a class="anchor-link" href="#Goal">&#182;</a></h5><p>"Lay down and place your phone on your chest.  Capture 10 minutes of normal breathing and
heart beats.  Can you write a function that takes this data to figure out your respiratory rate
(breaths per second) or heart rate?" -A3</p>
<p>In order to achieve this three processes needed to be developed:</p>
<ol>
<li>A Low Pass Filter, to remove the noise from the data.</li>
<li>FFT functions to gain access to various data. *Such as Pitch Detection</li>
<li>A Pitch Detection and Conversion tool.</li>
</ol>

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<h5 id="Low-Pass-Filter-+-FFT">Low Pass Filter + FFT<a class="anchor-link" href="#Low-Pass-Filter-+-FFT">&#182;</a></h5><p>It was necessary to use a windowing function in order to properly divide the data up into bins.  This will enable the filter to reduce high frequency content.  It will also allow it to remove gaussian noise:</p>
<div class="highlight"><pre><span></span><span class="n">win</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">hann</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span> <span class="c1">#LP Filter using hanning window </span>
<span class="n">yFilt</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">convolve</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">win</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">)</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">win</span><span class="p">)</span>
</pre></div>
<p>In order to test this filter a basic complex waveform was computed using the sum of sines.</p>
<div class="highlight"><pre><span></span><span class="n">y</span> <span class="o">=</span> <span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">ff</span><span class="o">*</span><span class="n">t</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">y</span> <span class="o">+</span> <span class="o">.</span><span class="mi">6</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="mi">4</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">ff</span><span class="o">*</span><span class="n">t</span><span class="p">)</span> <span class="o">+</span> <span class="o">.</span><span class="mi">4</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="mi">8</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">ff</span><span class="o">*</span><span class="n">t</span><span class="p">)</span> <span class="o">+</span> <span class="o">.</span><span class="mi">2</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="mi">12</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">ff</span><span class="o">*</span><span class="n">t</span><span class="p">)</span> <span class="c1">#summing sines</span>
</pre></div>
<p><img src="img/complexwave.png" alt="title">
This demonstrates the filter is smoothing out the waveform and removing high frequency content.  The blue x's represent the original peak energy per frequency.  While we can visually ascertain the pitch is 30 Hz we need to code a basic pitch detection algorithm. Once we can extract the fundamental frequency we can use that later on to figure out Breaths per Minute.</p>
<h5 id="Pitch-Detection">Pitch Detection<a class="anchor-link" href="#Pitch-Detection">&#182;</a></h5><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">pitchDetection</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">t</span><span class="p">,</span><span class="n">title</span><span class="p">):</span>
    <span class="n">yfft</span> <span class="o">=</span> <span class="n">fft</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
    <span class="n">FFT</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">y</span><span class="p">))</span>
    <span class="n">freqs</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">fftpack</span><span class="o">.</span><span class="n">fftfreq</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span>

    <span class="c1">#replace negative values</span>
    <span class="n">FFT</span><span class="p">[</span><span class="nb">abs</span><span class="p">(</span><span class="n">FFT</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">0.000001</span><span class="p">]</span><span class="o">=</span> <span class="mi">0</span> <span class="c1">#some zeros</span>
    <span class="n">FFT</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ma</span><span class="o">.</span><span class="n">masked_equal</span><span class="p">(</span><span class="n">FFT</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>

    <span class="n">maxPos</span> <span class="o">=</span> <span class="n">FFT</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="c1">#finds position in FFT with highest value = most energy</span>
    <span class="n">fundamentalFreq</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">freqs</span><span class="o">.</span><span class="n">real</span><span class="p">[</span><span class="n">maxPos</span><span class="p">])</span> <span class="c1">#uses maxPos to find the corresponding fundamental freq</span>
    <span class="k">print</span><span class="p">(</span><span class="s1">&#39;Fundamental Frequency Sine Wave &#39;</span><span class="p">,</span><span class="n">title</span><span class="p">,</span><span class="s1">&#39;= &#39;</span><span class="p">,</span> <span class="n">fundamentalFreq</span><span class="p">,</span> <span class="s1">&#39; Hz (Beats per Second)&#39;</span><span class="p">)</span>
</pre></div>

<pre><code>Fundamental Frequency Sine Wave  Normal =  30.0  Hz (Beats per Second)
Fundamental Frequency Sine Wave  Filtered =  30.0  Hz (Beats per Second)</code></pre>
<h5 id="Run-on-Breathing-Data">Run on Breathing Data<a class="anchor-link" href="#Run-on-Breathing-Data">&#182;</a></h5><p>After I completed collecting my data using AndroSensor on Android. I tookout a 10 minute section from the middle.  Instead of plotting relationships in Excel/Sheets I laid the phone on my chest and sat in a position where I could read the sensors.  I then carefull went through and looked at each sensor in real time.  What I was looking for were sensors who appeared to have nice sinusoidal waveforms on the application's display.  From this excercise I chose two:</p>
<p><img src="img/accXlong2.png" alt="title">
<img src="img/gyroYlong2.png" alt="title"></p>
<p>The two images above are scaled form -1 to 1.  From the images above the LP Filter does an excellent job of smoothing out the peaks and reducing noise.  The data itself and the algorithm work fairly well on their own:</p>
<p>Scaled -1 to 1 to represent waveform: (hann.window(50))</p>

<pre><code>Fundamental Frequency  Gyroscope Y =  [ 21.88]  Breaths per Minute (Avg Adult is 12-18)
Fundamental Frequency  Acceleration X =  [ 29.14]  Breaths per Minute (Avg Adult is 12-18)
Fundamental Frequency  Gyroscope Y - Filtered  =  [ 20.84]  Breaths per Minute (Avg Adult is 12-18)
Fundamental Frequency  Acceleration X - Filtered  =  [ 29.66]  Breaths per Minute (Avg Adult is 12-18)</code></pre>
<p>Not Scaled Raw Data: (hann.window(50))</p>

<pre><code>Fundamental Frequency  Gyroscope Y =  [ 21.88]  Breaths per Minute (Avg Adult is 12-18)
Fundamental Frequency  Acceleration X =  [ 20.75]  Breaths per Minute (Avg Adult is 12-18)
Fundamental Frequency  Gyroscope Y - Filtered  =  [ 20.55]  Breaths per Minute (Avg Adult is 12-18)
Fundamental Frequency  Acceleration X - Filtered  =  [ 20.69]  Breaths per Minute (Avg Adult is 12-18)</code></pre>
<p>The data is fairly accurate.  I used a hanning window of 50 to help smooth out the rough peaks.  I kept increasing the hanning window all the way up to 800.  It got both readings down to 18 and 19 breaths per minute.  However this data was too smoothed to be taken as truth.  A really good way to further explore the data is to pull out various chunks from the 6000 rows:
<img src="img/gyro_50_250.png" alt="title">
hann.window(20)</p>

<pre><code>Fundamental Frequency  Gyroscope Y =  [ 0.3]  Breaths per Minute (Avg Adult is 12-18)
Fundamental Frequency  Gyroscope Y - Filtered  =  [ 14.7]  Breaths per Minute (Avg Adult is 12-18)</code></pre>
<p><img src="img/acc1900_2000.png" alt="title">
hann.window(20)</p>

<pre><code>Fundamental Frequency  Acceleration X =  [ 22.2]  Breaths per Minute (Avg Adult is 12-18)]
Fundamental Frequency  Acceleration X - Filtered  =  [ 17.4]  Breaths per Minute (Avg Adult is 12-18)</code></pre>
<h5 id="Final-Thoughts">Final Thoughts<a class="anchor-link" href="#Final-Thoughts">&#182;</a></h5><p>We can see from these two examples that the filtering can work both ways to increase the accuracy on smaller samples sizes.  These methods are not full proof.  They tend to work best with Low Frequency waveforms.  Generally anything below 45 Hz.  Filtering helps for higher waveforms but there is always a tradeoff.  Something that is nice, is that the algorithm scales as you modify your sample size.  Hence why the various graphs above worked with different sample sizes.  The general range of results for individual snippets runs from ~0.5 to 30.0 beats per minute.</p>
<p>*My code runs on my local machine.  There are a few general warnings due to certain data handling methods that have started to be deprecated in newer versions of Python.  If you have any questions please do not hesitate to contact me.</p>

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<div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">sklearn</span> <span class="kn">as</span> <span class="nn">sk</span>
<span class="kn">import</span> <span class="nn">scipy</span> <span class="kn">as</span> <span class="nn">sp</span>
<span class="kn">import</span> <span class="nn">pylab</span>

<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">preprocessing</span>
<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">sin</span><span class="p">,</span> <span class="n">linspace</span><span class="p">,</span> <span class="n">pi</span>
<span class="kn">from</span> <span class="nn">pylab</span> <span class="kn">import</span> <span class="n">plot</span><span class="p">,</span> <span class="n">show</span><span class="p">,</span> <span class="n">title</span><span class="p">,</span> <span class="n">xlabel</span><span class="p">,</span> <span class="n">ylabel</span><span class="p">,</span> <span class="n">subplot</span>
<span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">fft</span><span class="p">,</span> <span class="n">arange</span><span class="p">,</span> <span class="n">signal</span>

<span class="k">def</span> <span class="nf">plotSpectrum</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">Fs</span><span class="p">,</span> <span class="n">color</span><span class="p">):</span>
    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="c1"># length of the signal</span>
    <span class="n">k</span> <span class="o">=</span> <span class="n">arange</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
    <span class="n">T</span> <span class="o">=</span> <span class="n">n</span><span class="o">/</span><span class="n">Fs</span>
    <span class="n">frq</span> <span class="o">=</span> <span class="n">k</span><span class="o">/</span><span class="n">T</span> <span class="c1"># two sides frequency range</span>
    <span class="n">frq</span> <span class="o">=</span> <span class="n">frq</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="n">n</span><span class="o">/</span><span class="mi">2</span><span class="p">]</span> <span class="c1"># one side frequency range (sliced the frq in half)</span>

    <span class="n">Y</span> <span class="o">=</span> <span class="n">fft</span><span class="p">(</span><span class="n">y</span><span class="p">)</span><span class="o">/</span><span class="n">n</span> <span class="c1"># fft computing and normalization</span>
    <span class="n">Y</span> <span class="o">=</span> <span class="n">Y</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="n">n</span><span class="o">/</span><span class="mi">2</span><span class="p">]</span>

    <span class="n">plot</span><span class="p">(</span><span class="n">frq</span><span class="p">,</span><span class="nb">abs</span><span class="p">(</span><span class="n">Y</span><span class="p">),</span><span class="n">color</span><span class="p">)</span> <span class="c1"># plotting the spectrum</span>
    <span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Freq (Hz)&#39;</span><span class="p">)</span>
    <span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;|Y(freq)|&#39;</span><span class="p">)</span>

<span class="k">def</span> <span class="nf">pitchDetection</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">t</span><span class="p">,</span><span class="n">title</span><span class="p">):</span>
    <span class="n">FFT</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">y</span><span class="p">))</span>
    <span class="n">freqs</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">fftpack</span><span class="o">.</span><span class="n">fftfreq</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="n">t</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">t</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>

    <span class="c1">#replace negative values</span>
    <span class="n">FFT</span><span class="p">[</span><span class="nb">abs</span><span class="p">(</span><span class="n">FFT</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">0.000001</span><span class="p">]</span><span class="o">=</span> <span class="mi">0</span> <span class="c1"># some zeros</span>
    <span class="n">FFT</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ma</span><span class="o">.</span><span class="n">masked_equal</span><span class="p">(</span><span class="n">FFT</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
    <span class="n">maxPos</span> <span class="o">=</span> <span class="n">FFT</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="c1">#finds position in FFT with highest value = most energy</span>
    <span class="n">fundamentalFreq</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">freqs</span><span class="o">.</span><span class="n">real</span><span class="p">[</span><span class="n">maxPos</span><span class="p">])</span> <span class="c1">#uses maxPos to find the corresponding fundamental freq</span>
    <span class="k">print</span><span class="p">(</span><span class="s1">&#39;Fundamental Frequency Sine Wave &#39;</span><span class="p">,</span><span class="n">title</span><span class="p">,</span><span class="s1">&#39;= &#39;</span><span class="p">,</span> <span class="n">fundamentalFreq</span><span class="p">,</span> <span class="s1">&#39; Hz (Beats per Second)&#39;</span><span class="p">)</span>


<span class="k">def</span> <span class="nf">pitchDetectionData</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">t</span><span class="p">,</span><span class="n">title</span><span class="p">):</span>
    <span class="n">yfft</span> <span class="o">=</span> <span class="n">fft</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>

    <span class="n">FFT</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">y</span><span class="p">))</span>
    <span class="n">freqs</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">fftpack</span><span class="o">.</span><span class="n">fftfreq</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span>

    <span class="c1">#replace negative values</span>
    <span class="n">FFT</span><span class="p">[</span><span class="nb">abs</span><span class="p">(</span><span class="n">FFT</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">0.000001</span><span class="p">]</span><span class="o">=</span> <span class="mi">0</span> <span class="c1"># some zeros</span>
    <span class="n">FFT</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ma</span><span class="o">.</span><span class="n">masked_equal</span><span class="p">(</span><span class="n">FFT</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>

    <span class="n">maxPos</span> <span class="o">=</span> <span class="n">FFT</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="c1">#finds position in FFT with highest value = most energy</span>
    <span class="n">fundamentalFreq</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">freqs</span><span class="o">.</span><span class="n">real</span><span class="p">[</span><span class="n">maxPos</span><span class="p">])</span> <span class="c1">#uses maxPos to find the corresponding fundamental freq</span>
    <span class="k">print</span><span class="p">(</span><span class="s1">&#39;Fundamental Frequency &#39;</span><span class="p">,</span><span class="n">title</span><span class="p">,</span><span class="s1">&#39;= &#39;</span><span class="p">,</span> <span class="n">fundamentalFreq</span><span class="o">*</span><span class="mi">60</span><span class="p">,</span> <span class="s1">&#39; Breaths per Minute (Avg Adult is 12-18)&#39;</span><span class="p">)</span>

<span class="c1">###START-PROOF#####################################################################</span>
<span class="n">Fs</span> <span class="o">=</span> <span class="mf">100.0</span><span class="p">;</span>  <span class="c1"># sampling rate</span>
<span class="n">Ts</span> <span class="o">=</span> <span class="mf">1.0</span><span class="o">/</span><span class="n">Fs</span><span class="p">;</span> <span class="c1"># sampling interval</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="n">Ts</span><span class="p">)</span> <span class="c1"># time vector</span>

<span class="n">ff</span> <span class="o">=</span> <span class="mi">30</span><span class="p">;</span>   <span class="c1"># frequency of the test signal</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">ff</span><span class="o">*</span><span class="n">t</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">y</span> <span class="o">+</span> <span class="o">.</span><span class="mi">6</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="mi">4</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">ff</span><span class="o">*</span><span class="n">t</span><span class="p">)</span> <span class="o">+</span> <span class="o">.</span><span class="mi">4</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="mi">8</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">ff</span><span class="o">*</span><span class="n">t</span><span class="p">)</span> <span class="o">+</span> <span class="o">.</span><span class="mi">2</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="mi">12</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">ff</span><span class="o">*</span><span class="n">t</span><span class="p">)</span> <span class="c1">#summing sines</span>

<span class="n">win</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">hann</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span> <span class="c1">#LP Filter using hanning window</span>
<span class="n">yFilt</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">convolve</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">win</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">)</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">win</span><span class="p">)</span>

<span class="c1">#compute FFT</span>
<span class="n">yfft</span> <span class="o">=</span> <span class="n">fft</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="n">FFT</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">y</span><span class="p">))</span>
<span class="n">freqs</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">fftpack</span><span class="o">.</span><span class="n">fftfreq</span><span class="p">(</span><span class="n">t</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="n">t</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">t</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="c1">#replace negative values</span>
<span class="n">FFT</span><span class="p">[</span><span class="nb">abs</span><span class="p">(</span><span class="n">FFT</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">0.000001</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># some zeros</span>
<span class="n">FFT</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ma</span><span class="o">.</span><span class="n">masked_equal</span><span class="p">(</span><span class="n">FFT</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>


<span class="n">pitchDetection</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">t</span><span class="p">,</span><span class="s1">&#39;Normal&#39;</span><span class="p">)</span>
<span class="n">pitchDetection</span><span class="p">(</span><span class="n">yFilt</span><span class="p">,</span><span class="n">t</span><span class="p">,</span><span class="s1">&#39;Filtered&#39;</span><span class="p">)</span>

<span class="n">pylab</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">212</span><span class="p">)</span>
<span class="n">pylab</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">freqs</span><span class="o">.</span><span class="n">real</span><span class="p">),</span> <span class="n">sp</span><span class="o">.</span><span class="n">log10</span><span class="p">(</span><span class="n">FFT</span><span class="p">),</span> <span class="s1">&#39;x&#39;</span><span class="p">)</span>

<span class="n">subplot</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="n">y</span><span class="p">,</span> <span class="s1">&#39;g&#39;</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="n">yFilt</span><span class="p">,</span> <span class="s1">&#39;r&#39;</span><span class="p">)</span>
<span class="n">title</span><span class="p">(</span><span class="s1">&#39;Complex Waveform - 30 Hz&#39;</span><span class="p">)</span>
<span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Time&#39;</span><span class="p">)</span>
<span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Amplitude&#39;</span><span class="p">)</span>
<span class="n">subplot</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
<span class="n">plotSpectrum</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">Fs</span><span class="p">,</span> <span class="s1">&#39;g&#39;</span><span class="p">)</span>
<span class="n">plotSpectrum</span><span class="p">(</span><span class="n">yFilt</span><span class="p">,</span><span class="n">Fs</span><span class="p">,</span> <span class="s1">&#39;r&#39;</span><span class="p">)</span>
<span class="n">show</span><span class="p">()</span>

<span class="c1">###START-DATA##################################################################</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">genfromtxt</span><span class="p">((</span><span class="s1">&#39;_DataRaw/Breathing.csv&#39;</span><span class="p">),</span> <span class="n">delimiter</span><span class="o">=</span><span class="s1">&#39;,&#39;</span><span class="p">,</span> <span class="n">skip_header</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>

<span class="n">scaler</span> <span class="o">=</span> <span class="n">preprocessing</span><span class="o">.</span><span class="n">MinMaxScaler</span><span class="p">([</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span> <span class="c1">#fits better with pitch detection</span>

<span class="n">mnL</span> <span class="o">=</span> <span class="mi">750</span>
<span class="n">mxL</span> <span class="o">=</span> <span class="mi">950</span>
<span class="n">mnL</span> <span class="o">=</span> <span class="mi">1000</span>
<span class="n">mxL</span> <span class="o">=</span> <span class="mi">1400</span>
<span class="n">mnL</span> <span class="o">=</span> <span class="mi">1900</span>
<span class="n">mxL</span> <span class="o">=</span> <span class="mi">2300</span>
<span class="n">mnL</span> <span class="o">=</span> <span class="mi">1900</span>
<span class="n">mxL</span> <span class="o">=</span> <span class="mi">2000</span>
<span class="n">mnL</span> <span class="o">=</span> <span class="mi">50</span>
<span class="n">mxL</span> <span class="o">=</span> <span class="mi">250</span>
<span class="n">time</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">mnL</span><span class="p">:</span><span class="n">mxL</span><span class="p">,</span><span class="mi">18</span><span class="p">]</span>
<span class="c1">#accelX = scaler.fit_transform(data[mnL:mxL, 0])</span>
<span class="c1">#gyroY = scaler.fit_transform(data[mnL:mxL, 10])</span>
<span class="n">accelX</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">mnL</span><span class="p">:</span><span class="n">mxL</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
<span class="n">gyroY</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">mnL</span><span class="p">:</span><span class="n">mxL</span><span class="p">,</span> <span class="mi">10</span><span class="p">]</span>

<span class="n">win</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">hann</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span>
<span class="n">accelXFilt</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">convolve</span><span class="p">(</span><span class="n">accelX</span><span class="p">,</span> <span class="n">win</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">)</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">win</span><span class="p">)</span>
<span class="n">gyroYFilt</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">convolve</span><span class="p">(</span><span class="n">gyroY</span><span class="p">,</span> <span class="n">win</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">)</span> <span class="o">/</span> <span class="nb">sum</span><span class="p">(</span><span class="n">win</span><span class="p">)</span>

<span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">time</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">time</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">accelX</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">accelX</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">accelX</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">gyroY</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">gyroY</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">gyroY</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">accelXFilt</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">accelXFilt</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">accelXFilt</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">gyroYFilt</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">gyroYFilt</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">gyroYFilt</span><span class="p">),</span> <span class="mi">1</span><span class="p">)</span>

<span class="n">pitchDetectionData</span><span class="p">(</span><span class="n">gyroY</span><span class="p">,</span><span class="n">time</span><span class="p">,</span><span class="s1">&#39;Gyroscope Y&#39;</span><span class="p">)</span>
<span class="n">pitchDetectionData</span><span class="p">(</span><span class="n">accelX</span><span class="p">,</span><span class="n">time</span><span class="p">,</span><span class="s1">&#39;Acceleration X&#39;</span><span class="p">)</span>
<span class="n">pitchDetectionData</span><span class="p">(</span><span class="n">gyroYFilt</span><span class="p">,</span><span class="n">time</span><span class="p">,</span><span class="s1">&#39;Gyroscope Y - Filtered &#39;</span><span class="p">)</span>
<span class="n">pitchDetectionData</span><span class="p">(</span><span class="n">accelXFilt</span><span class="p">,</span><span class="n">time</span><span class="p">,</span><span class="s1">&#39;Acceleration X - Filtered &#39;</span><span class="p">)</span>

<span class="n">title</span><span class="p">(</span><span class="s1">&#39;Acceleration X &#39;</span><span class="p">)</span>
<span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Filtered (blue) &amp; Normal (green)&#39;</span><span class="p">)</span>
<span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Time&#39;</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">accelX</span><span class="p">,</span> <span class="s1">&#39;y&#39;</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">accelXFilt</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">)</span>
<span class="n">show</span><span class="p">()</span>

<span class="n">title</span><span class="p">(</span><span class="s1">&#39;Gyroscope Y&#39;</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">gyroY</span><span class="p">,</span> <span class="s1">&#39;y&#39;</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">gyroYFilt</span><span class="p">,</span> <span class="s1">&#39;b&#39;</span><span class="p">)</span>
<span class="n">show</span><span class="p">()</span>
</pre></div>

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